Maslov index in semi-Riemannian submersions

We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the projected geodesic pi omicron gamma : I -> B in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary spacetime which is orthogonal to a timelike Killing vector field.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

Major determinants of photoinduced cell death: Subcellular localization versus photosensitization efficiency

We present a study on whether and to what extent subcellular localization may compete favorably with photosensitization efficiency with respect to the overall efficiency of photoinduced cell death. We have compared the efficiency with which two cationic photosensitizers, namely methylene blue (MB) and crystal violet (CV), induce the photoinduced death of human cervical adenocarcinoma (HeLa) cells. Whereas MB is well known to generate singlet oxygen and related triplet excited species with high quantum yields in a variety of biological and chemical environments (i.e., acting as a typical type II photosensitizer), the highly mitochondria-specific CV produces triplet species and singlet oxygen with low yields, acting mostly via the classical type I mechanism (e.g., via free radicals). The findings described here indicate that the presumably more phototoxic type II photosensitizer (MB) does not lead to higher degrees of cell death compared to the type I (CV) photosensitizer. In fact, CV kills cells with the same efficiency as MB, generating at least 10 times fewer photoinduced reactive species. Therefore, subcellular localization is indeed more important than photochemical reactivity in terms of overall cell killing, with mitochondrial localization representing a highly desirable property for the development of more specific/efficient photosensitizers for photodynamic therapy applications. (C) 2011 Elsevier Inc. All rights reserved.

The importance of protoporphyrin IX efflux for ALA-PDT dosimetry

One of the major advances in PDT is the use of 5-aminolevulinic acid (ALA) to induce the production of an enclogenous photosensitizer inside the cells using intracellular enzymatic pathways. ALA is the first intermediate in heme biosynthesis and a precursor of the protoporphyrin IX (PpIX). When activated by light, this efficient photosensitizer accumulated in the target cells can produce cytotoxicity. The aim of this study was to find the best conditions for cell killing using ALA to temporarily increase the concentration of PpIX in two cell lines. It was shown that a considerable efflux of synthesized PpIX occurs. Since this efflux is time-dependent, it is essential to know the optimum time for irradiation after ALA administration. So, the efflux of PpIX from the cells is an important parameter to be considered for ALA-PDT dosimetry.